ﻻ يوجد ملخص باللغة العربية
The Cancellation Problem for Affine Spaces is settled affirmatively, that is, it is proved that : Let $ k $ be an algebraically closed field of characteristic zero and let $n, m in mathbb{N}$. If $R[Y_1,..., Y_m] cong_k k[X_1,..., X_{n+m}]$ as $k$-algebras, where $Y_1,..., Y_m, X_1,..., X_{n+m}$ are indeterminates, then $R cong_k k[X_1,..., X_n]$.
We have proved the following Problem:{it Let $R$ be a $mathbb{C}$-affine domain, let $T$ be an element in $R setminus mathbb{C}$ and let $i : mathbb{C}[T] hookrightarrow R$ be the inclusion. Assume that $R/TR cong_{mathbb{C}} mathbb{C}^{[n-1]}$ and t
We prove estimates for the level of distribution of the Mobius function, von Mangoldt function, and divisor functions in squarefree progressions in the ring of polynomials over a finite field. Each level of distribution converges to $1$ as $q$ goes t
Let K be a finite field and let X* be an affine algebraic toric set parameterized by monomials. We give an algebraic method, using Groebner bases, to compute the length and the dimension of C_X*(d), the parameterized affine code of degree d on the se
We provide a number of new conjectures and questions concerning the syzygies of $mathbb{P}^1times mathbb{P}^1$. The conjectures are based on computing the graded Betti tables and related data for large number of different embeddings of $mathbb{P}^1ti
In this note we study and obtain factorization theorems for colorings of matrices and Grassmannians over $mathbb{R}$ and ${mathbb{C}}$, which can be considered metr